Saturday, May 06, 2017

Techmania: physics fun but something is missing without the maths

On Friday, we spent almost five hours in Techmania, Pilsen's science center built on the land that belonged to Škoda Works: the Pilsner episode of War of Tanks (where tanks can fly) is taking place almost exactly in Techmania. The only Czech 3D planetarium is a part of the facility. With a friend, we went to the planetarium last year or so.

But I haven't seen the main expositions for more than 2 years. So yesterday I could see that things got much more polished (even though you can still see in most of the area that the place used to be a factory), some gadgets were added. Sadly, some helpful gadgets have apparently disappeared, too.

Such a science center is full of gadgets that demonstrate some basic phenomena and principles of physics. You may create sound and light waves, combine colors, sink a submarine with bubbles, create huge vortices, check how polarized sound and light gets transmitted or absorbed, rotate a one-ton spherical marble with your finger (because there are water currents beneath it), check how sound gets reflected from a parabolic mirror (by talking to your friend who is 20 meters away), play with numerous machines that have resonance frequencies and the resonances get manifested in many ways, and literally hundreds of similar things.

There is a dodecathlon – physics-optimized variations of skiing, shooting, floorball etc. I won all these disciplines that we tried which is nice for a guy who usually isn't considered a top athlete (not even by myself LOL). Also, all of us tried the astronauts' gyroscope (or centrifuge) which was rather pleasant and I didn't want to vomit at all. David Černý's Entropa is still there – and it's finally exposed so that no one overlooks it.

I think that some X-ray machines have disappeared – a major example of negative developments.

On the other hand, there were some new exhibitions such as one dedicated to the geology, rocks, and miners; and the nutrition value of food. The geological section was sufficiently insightful and entertaining, too. But we found the exhibition about food to be a waste of time. You don't need a science museum to understand that meat has some proteins but potato chips contain more kilocaries than vegetable etc. The food exhibition is aesthetically pleasing but the content seems almost non-existent. But let me admit that we didn't study it carefully. Nevertheless, it seems to me that someone just said that "biology" should also be there, someone else said "food", and then they paid some money to someone to produce 30 pieces of a food exhibition – while not thinking whether it would be insightful and amusing at all. Well, it isn't too insightful or amusing and most of the things over there look the same.

There are lots of cool effects and some of the machines look almost magical. Children as well as adults may play with them, get amused, and even understand some basic principles of physics – usually classical physics. Well, similar school-level and bit better experimental demonstrations are almost always revolving around classical physics. I think that some modern physics and quantum mechanics in particular could also be there but it's (almost?) absent.

Children that visit the science center may be driven closer to physics – and to engineering.

But even if the selection of the physical phenomena were perfect, if the redundant exhibitions were reduced and the missing ones were added, I am still afraid that centers like that may be played with in ways that "aren't really scientific".

When a person sees an interesting physical effect demonstrated by a device, he or she may demand different levels of understanding what's going on and why. Most people can train themselves to agree with their eyes. They see (or hear) that some physical situation does something under some circumstances. Electromagnetic induction works. Water in a tube with some sound starts to create showers at particular places. Add hundreds of other examples. Someone may say "this and that will happen", it indeed happens, and he may be satisfied with the "explanation".

But many of these people haven't given any explanation at all. They just said that something was happening. But why was it happening? Did they reduce it to some simpler axioms or laws of physics? And even the more sophisticated ones sometimes only reduce the effects to something that is still very far from the fundamental laws of physics or the "first principles". Some of this superficial approach may be enough for future engineers but physicists should go deeper.

At the end, the physicists' understanding requires the reduction of the effects to some equations that have a chance to be considered fundamental. And a person claiming to be a master of such equations of physics must not only know why they're relevant in a particular demonstration. He should also be able to solve some of these equations – at least approximately or qualitatively etc. – so that he may explain some other, perhaps more complex situations than the elementary ones that are shown in Techmania.

To summarize, I believe that such science centers are good to bring schoolkids closer to physics and engineering. But to turn them into engineers and especially physicists, one simply needs some mathematical attitude and lots of mathematical practice, too. And this mathematical layer of the education – and the depth with which students are expected to think about rather simple questions, such as one gadget in the Techmania exhibitions – is gradually disappearing.

Several days ago, someone at Quantum Frontiers asked the readers whether physics education should be modernized and what the new one should contain. Over the years, we have written lots of things about the desire to bring quantum mechanics to high schools if not basic schools, about the right way to teach quantum mechanics and its conceptual foundations and other things. There are surely relatively new insights that are underdiscussed at schools – and underdemonstrated in places like Techmania. Many newer insights could be taught – and some older ones, no longer considered important, relevant, or fundamental, could also be removed.

However, my feeling is that most of the evolution is ultimately going in the negative direction. Many of the changes end up making physics education "more connected with the present era" and its fashions. The desire to be hip is often treated as a top priority. The unavoidable result is that aspects that are really important are suppressed.

When "contemporary" topics are being taught most of the time, the students unavoidably lose much of their understanding of how these often composite and complex things are connected with the fundamental laws of Nature; or how they (e.g. some machines) have developed. Why do we have them at all? I find these growing gaps troubling. An engineer may be trained to work with some particular machines (or even software) that have only existed for a few years or at most decades. But they won't understand how they could have been built at all etc.

It may often be a great idea to focus on the study of old things. Even when some of these things seem obsolete, the education discussing them may be classified as a lecture on history. But history of physics and engineering is more than just the history itself. The history is a key to the present state of affairs, too. If some principles and concepts may be taught using the examples or logic that were actually important historically, it should be the preferred way because the students learn the principles as well as their origin.

And then there are examples of changes that are downright crippling. The likes of Paul Dirac – and his smart students – understood the foundations of quantum mechanics but lots of people currently teaching these things are utterly confused about extremely rudimentary facts, e.g. the very fact that quantum mechanics cannot be formulated as a classical, i.e. observer-independent, theory. If they're confused, shouldn't they be at least able to admit that their pedagogic package is inferior relatively to Dirac's and we should teach Dirac's instead? Unfortunately, that's not happening. When two possible syllabuses are being compared, the "more modern one" is often considered the winner even if it is the loser according to the meritocratic criteria. Paul Dirac was born in 1902 and a physics professor born after 1902 may be expected to know better. Except that he often doesn't. It's too bad that it's often being assumed that the explanations made by the people born after 1902 are inevitably better than those written by the people born in 1902 – just because of the comparison of the birth dates. Progress exists in many situations but it's totally wrong to treat progress as if it were an axiom – a universal rule saying that explanations made later or by younger people are better than the older ones prepared by the older people. Progress that would be this reliable and universal clearly doesn't exist.

Commenters at the Quantum Frontiers blog propose lots of things that should be taught. Mason42 wrote:

The physics curriculum spends way too much time on linear things and not enough time on nonlinear ones. There are a lot more of the latter...

I think that this opinion is largely a myth, too. You may take a straight line and bend it – turn it into a hyperbola, for example – and that's a way to "generalize" certain objects. In this case, we are replacing a linear object with a nonlinear one.

But this is a sort of a "very simple" and usually "not very deep" and even "not very useful" generalization. (Special relativity as a replacement of Newtonian-Galilean spacetime may be considered an exception. But note that relativity isn't just a generic nonlinear deformation of the non-relativistic formulae; it is a very special one that is at least as constrained as the simple linear, non-relativistic formulae.) This is how people were imagining progress in physics up to the 19th century. The equations of classical physics may have been deformed by the addition of new terms. Maxwell's equations are linear in the electric and magnetic fields but they may be made non-linear, too. Think about the Dirac-Born-Infeld action etc.

However, the actual progress in physics included much more dramatic changes than the replacement of linear structures with nonlinear ones. Quantum mechanics has replaced commuting observable with non-commuting ones, observer-independent facts with facts that depend on the choice of the observer and his perspective (which determines what is an observation, what isn't, and what the results of the observations have been). This is a much harder change to understand than the addition of some nonlinear corrections to linear equations.

Moreover, quantum mechanics actually made precisely linear equations more important and true than ever before. All observables must be connected with linear operators on the Hilbert space. And the wave function or density matrix evolved according to exactly linear equations, too.

The operators typically follow nonlinear (Heisenberg) equations of motion. But lots of their important properties are already contained in the simplified, often linear toy models or integrable models. The deformation by new terms is the "least interesting" part of the story. It's arguably the integrable, simplest, zeroth-order models and methods that contain most of the true qualitative wisdom. So I simply disagree with the thesis that "most of the things that are taught should be nonlinear" or "students should be taught that the bulk of the physical wisdom is nonlinear". It's not. I could give you many other examples. Linear regression is arguably more important than the most general nonlinear fits, too. Most effects in the world are mixtures and nonlinear deformations but physics is a reductionist enterprise that wants to isolate the "pure flavors" and "elements of wisdom" and many or most of these are "linear" or otherwise crisp and simple. To fail to appreciate those means to spit on reductionism and the basic spirit of physics in general.

Xuan Qin wrote:

Quantum information. A qubit is simple. A quantum mechanics course needn’t be a veiled introduction to linear differential equations and greens functions. Even if your end goal is to understand quantum field theory, one could conceptually outline all the important ideas in quantum mechanics using a qubit with very simple linear algebra of 2×2 matrices.

Well, I am more sympathetic to this one. Two-level systems contain most of the actual novelties that quantum mechanics brought us. These two-level systems also form a big part of the quantum mechanical volume of the Feynman Lectures in Physics. I think that it was a good approach – although not the only good approach – to the teaching of quantum mechanics.

However, what I don't like is what people usually add to the two-level systems in 2017. They usually add the thesis that the world fundamentally prefers base-two information or that theories based on qubits are or would be more fundamental. Well, Nature doesn't find the base-two systems natural at all and having base-two building blocks doesn't make a theory fundamental, either.

And indeed, the Feynman Lectures in Physics didn't contain the word "qubit" or the phrase "quantum bit". After all, these phrases weren't used in 1964. That's why. ;-) But the real justification of the two-level systems is that two is the minimum dimension of a Hilbert space on which the operators are non-commuting. One-dimensional operators are commuting – 1x1 matrices are equivalent to \(c\)-numbers. So the two-level systems may be picked as an example because the corresponding vectors and matrices contain the minimum number of complex numbers that are consistent with the existence of non-commuting operators. And it's easier for humans to calculate with matrices that only contain 4 matrix elements. However, unlike humans, Nature isn't afraid of adding the fifth or ninth matrix element or infinitely many. The simplification of the two-level systems is purely pedagogical: there is absolutely no physical reason to think that these systems are preferred by Nature Herself.

Various things may be added and subtracted but I think that a comparison of the education in the 1930s – or even 1890s – with the current one indicates that the net change of the education has been a counterproductive one. While improvements and helpful modernization are possible, they seem unlikely. For that reason, I think that the preservation of the education as it worked in the past is better than the type of modernization that the real-world people in the contemporary world are likely to propose and defend.